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GCF of 12 and 33

GCF of 12 and 33 is the largest possible number that divides 12 and 33 exactly without any remainder. The factors of 12 and 33 are 1, 2, 3, 4, 6, 12 and 1, 3, 11, 33 respectively. There are 3 commonly used methods to find the GCF of 12 and 33 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 12 and 33
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 33?

Answer: GCF of 12 and 33 is 3.

Explanation:

The GCF of two non-zero integers, x(12) and y(33), is the greatest positive integer m(3) that divides both x(12) and y(33) without any remainder.

Methods to Find GCF of 12 and 33

Let's look at the different methods for finding the GCF of 12 and 33.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

GCF of 12 and 33 by Prime Factorization

Prime factorization of 12 and 33 is (2 × 2 × 3) and (3 × 11) respectively. As visible, 12 and 33 have only one common prime factor i.e. 3. Hence, the GCF of 12 and 33 is 3.

GCF of 12 and 33 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 33 and Y = 12

GCF(33, 12) = GCF(12, 33 mod 12) = GCF(12, 9)
GCF(12, 9) = GCF(9, 12 mod 9) = GCF(9, 3)
GCF(9, 3) = GCF(3, 9 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 12 and 33 is 3.

GCF of 12 and 33 by Long Division

GCF of 12 and 33 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 33 (larger number) by 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 12 and 33.

☛ Also Check:

GCF of 12 and 33 Examples

Example 1: For two numbers, GCF = 3 and LCM = 132. If one number is 12, find the other number.

Solution:

Given: GCF (y, 12) = 3 and LCM (y, 12) = 132
∵ GCF × LCM = 12 × (y)
⇒ y = (GCF × LCM)/12
⇒ y = (3 × 132)/12
⇒ y = 33
Therefore, the other number is 33.
Example 2: The product of two numbers is 396. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 396
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 396/3
Therefore, the LCM is 132.
Example 3: Find the GCF of 12 and 33, if their LCM is 132.

Solution:

∵ LCM × GCF = 12 × 33
⇒ GCF(12, 33) = (12 × 33)/132 = 3
Therefore, the greatest common factor of 12 and 33 is 3.

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FAQs on GCF of 12 and 33

What is the GCF of 12 and 33?

The GCF of 12 and 33 is 3. To calculate the greatest common factor of 12 and 33, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 33 = 1, 3, 11, 33) and choose the greatest factor that exactly divides both 12 and 33, i.e., 3.

What is the Relation Between LCM and GCF of 12, 33?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 12 and 33, i.e. GCF × LCM = 12 × 33.

How to Find the GCF of 12 and 33 by Prime Factorization?

To find the GCF of 12 and 33, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 33 = 3 × 11.
⇒ Since 3 is the only common prime factor of 12 and 33. Hence, GCF (12, 33) = 3.
☛ Prime Number

How to Find the GCF of 12 and 33 by Long Division Method?

To find the GCF of 12, 33 using long division method, 33 is divided by 12. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

If the GCF of 33 and 12 is 3, Find its LCM.

GCF(33, 12) × LCM(33, 12) = 33 × 12
Since the GCF of 33 and 12 = 3
⇒ 3 × LCM(33, 12) = 396
Therefore, LCM = 132
☛ GCF Calculator

What are the Methods to Find GCF of 12 and 33?

There are three commonly used methods to find the GCF of 12 and 33.

By Listing Common Factors
By Long Division
By Prime Factorization

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